All the inflatable SUPs I have seen have great big fat rails at the tail.
As a result they surf really badly.

Does anyone know of a board under 130 litres that has skinny rails above the fins?

[there is no need to tell me that when you blow things up they go to a round shape]

There are the hybrid boards. Someone will know the brand. They have a hard tail and an inflatable front half. They pack down to the size of a boogie board.
Dripping wet in Manly had a second hand one for sale a little while back.

There are also the uli boards that have a rubber rail glued to the back end.
I did get a shark 9 6 inflatable that has a narrow tail for surfing. It was actually very stiff and very high quality, and went ok. However like all inflatables they just will not glide like a hard board. I only used it a couple of times. You can have it for a cheap price eg $400 if you want it.

All the classically built inflatables boards will have the same thickness all over.

I know only 2 inflatable boards that have thinner rails:

- the hybrid, inflatable in front / hard shall in the tail boards by Fabien Pendle pendleboard.com/en/home/

- the new (I guess available in October) multi-chambered boards with plastic spheres in it: tripstix.de/technology/

Otherwise you can try to reduce the volume of the tail: with a narrow one as above, or with a Simmons shape where you can leave the rear foot on the leash plug without sinking the tail for added looseness.

Select to expand quote

colas said..
>> the new (I guess available in October) multi-chambered boards with plastic spheres in it: www.tripstix.de/technology/

Thanks for that. The Tripstix team were thinking what I was thinking with the addition of those vacuum sections; pump some bits, vacuum others (like a packet of coffee grounds).Anyway, the Kickstarter website says:

(July 5, 2017)
Successfully raised ?101,704 with 86 backers
..the project will go ahead.

Bit bulky when rolled up though..